Modified Breit–Wigner formula for mesonic resonances describing OZI decays of confined 
                $q\bar{q}$
               states and the light scalar mesons

Beveren, Eef van; Rupp, George

doi:10.1007/s100520100823

Cited by 55 publications

(82 citation statements)

References 38 publications

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“…For example, only through the hypothetical movements of the poles in the complex-energy plane we can show that the f 0 (600), f 0 (980), K * 0 (800) [26] and a 0 (980) are manifestations of the same phenomenon, but for different flavors [31].…”

Section: Unitarizationmentioning

confidence: 99%

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Explaining the D[sub sJ][sup ∗](2317)[sup +]

Beveren¹,

Rupp²

2003

AIP Conference Proceedings

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The recently observed D * sJ (2317) + meson is explained as a scalar cs system which appears as a bound state pole, below threshold, in the DK scattering amplitude. The standard cs charmed scalar D s0 is found at about 2.9 GeV, with a width of some 150 MeV.For the scattering length of DK in S wave we predict 5 ± 1 GeV −1 . IntroductionThe D * sJ (2317) + state has, since its discovery [1] by the BABAR collaboration (see also Refs. [2,3]), raised several interesting questions on its nature [4][5][6][7][8][9][10][11][12][13][14][15]. However, the light-scalar-meson hypothesis from unitarization [16] has made important progress with the discovery of the D * sJ (2317) + 1 state (most likely J = 0). Not often it happens that in experiment a state is discovered which seems difficult to handle within other theories [17][18][19][20][21], but can be explained by the unitarization hypothesis without extra ingredients.Of course, this happened before with the light scalar mesons, which can easily be handled within a unitarized model for all non-exotic mesons [22], without making any distinction between the heavier scalar mesons and the light ones. But seventeen years after the publication of these results [16], their implications are still not fully understood, nor applied in data analysis.In UnitarizationIn the unitarization scheme, we describe meson-meson scattering by the wave equationThe operators H f and H c respectively describe the dynamics of two free mesons and of a confined quark-antiquark system. The latter is supposed to generate an infinity of confinement states.Transitions from confined quarks to free mesons, mediated by quark-antiquark-pair creation, is described by V t .By comparison of Eq. (1) with the usual expressions for scattering wave equations, we conclude that the generalized potential V for meson-meson scattering is given byWith the definitions given in Appendix A, in particular formulae (7), (17) and Table 1, we obtain for the partial-wave scattering phase shift generated by wave equation (1) the resultThe expression (3), which is an exact solution of Eq. (1) Another, in practice very useful approximation is inspired by the radial dependence of the transition potential V t , which is depicted in Ref.[25] for meson-meson scattering in the cases− , and J P = 0 + , We find there that V t is peaked at short distances. If we, moreover, take into account that eigenfunctions of the confinement Hamiltonian H c must also be of short range, then we may just define a transition radius a and approximate the spatial integrals of formula (17) by choosing a spherical delta shell U(r) = δ(r − a). In this case we end up with the expressionThis way we have pulled the p dependence outside the infinite summation over the radial confinement spectrum, which makes it much easier to handle truncations, as now the rest term does not depend on p and may thus be chosen constant. Our recent detailed analyses of scalar mesons have actually been performed in the approximation of formula (4). Our understanding of the sc...

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Section: Unitarizationmentioning

confidence: 99%

“…[35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50], the κ(800) in Refs. [31,32,[51][52][53], the isovectors a 0 in Ref. [54,55], dynamically generated scalar mesons in Ref.…”

Section: The Scalar Mesonsmentioning

confidence: 99%

Explaining the D[sub sJ][sup ∗](2317)[sup +]

Beveren¹,

Rupp²

2003

AIP Conference Proceedings

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“…However, the study of non-ground-state D * s vector mesons requires a more elaborate approach than the one previously applied by us to scalar mesons [13], as we shall explain in the following.…”

Section: Introductionmentioning

confidence: 99%

Multichannel Calculation ofDs*Vector States and theDsJ+(2632)R

Beveren

Rupp

2004

Phys. Rev. Lett.

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We study bound states below threshold and resonances above threshold in the D 0 K + and D + s η systems, using a many-coupled-channel model for nonexotic meson-meson scattering applied to states with the quantum numbers of cs quark-antiquark vector mesons. We fit the ground state at 2.112 GeV, whence the lowest resonances in D 0 K + come out at 2.61, 2.72, 3.03, and 3.08 GeV. The resonance at 2.61 GeV acquires a width of about 8 MeV, while its partial P-wave cross section is up to six times larger in D s η than in D 0 K + , provided a mechanism accounting for Okubo-Zweig-Iizuka-forbidden decays is included. The latter finding is in agreement with the observations of the SELEX collaboration [1] with respect to the recently reported D + sJ (2632) resonance. Therefore, we conclude that the D + sJ (2632) is probably the first recurrence of the D * s (2112) meson.

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“…As a matter of fact, perhaps the most remarkable conquest of the model is its parameter-free prediction of the light scalar mesons [10], including the κ(800) (K * 0 ) [11], which has very recently been experimentally confirmed [12]. Precisely for the light scalars, perturbation theory manifestly breaks down [9,13].…”

Section: Introductionmentioning

confidence: 99%

Relativistic Unitarized Quark/Meson Model in Momentum Space

Rupp

Beveren

2003

AIP Conference Proceedings

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An outline is given how to formulate a relativistic unitarized constituent quark model of mesons in momentum space, employing harmonic quark confinement. As a first step, the momentum-space harmonic-oscillator potential is solved in a relativistically covariant, three-dimensional quasipotential framework for scalar particles, using the spline technique. Then, an illustrative toy model with the same dynamical equations but now one qq and one meson-meson channel, coupled to one another through quark exchange describing the 3 P 0 mechanism, is solved in closed form on a spline basis. Conclusions are presented on how to generalize the latter to a realistic multichannel quark/meson model.

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Modified Breit–Wigner formula for mesonic resonances describing OZI decays of confined $q\bar{q}$ states and the light scalar mesons

Cited by 55 publications

References 38 publications

Explaining the D[sub sJ][sup ∗](2317)[sup +]

Explaining the D[sub sJ][sup ∗](2317)[sup +]

Multichannel Calculation ofDs*Vector States and theDsJ+(2632)R

Relativistic Unitarized Quark/Meson Model in Momentum Space

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